SpecsVerification (version 0.4-1)

DressEnsemble: Ensemble dressing

Description

Transform an ensemble forecast to a continuous forecast distribution by kernel dressing.

Usage

DressEnsemble(ens, dressing.method, parameters)

Arguments

ens

matrix, N rows, K columns. An archive of K-member ensemble forecasts for N time instances.

dressing.method

string. One of "silverman" (default), "akd", "akd.fit". See Details.

parameters

list. Contains the parameters for the dressing method. See Details.

Value

The function returns an object of class `dressed.ensemble`, which is a list with elementsens: matrix, N rows, K columns. The element ens[n,k] is the mean of the `k`-th kernel at time instance `n`.ker.wd: matrix, N rows, K columns. The element ker.wd[n,k] is the standard deviation of the `k`-th kernel at time instance `n`.ker.type: string. Type of the dressing kernel.

Details

The dressing methods currently implemented and their required parameters are:

"silverman" (default): No parameters are given. At time instance `n` each ensemble member is replaced by a Gaussian kernel with mean ens[n, k] and variance (4 / 3 / K)^0.4 * var(ens[n, ]). This method is called "Silverman's rule of thumb" and provides a simple non-parametric method for smoothing a discrete ensemble.

"akd": Affine Kernel Dressing. The required parameters are list(r1, r2, a, s1, s2). The `k`-th ensemble member at time instance `n` is dressed with a Gaussian kernel with mean r1 + r2 * mean(ens[n,]) + a * ens[n, k] and variance (4 / 3 / K)^0.4 * (s1 + s2 * a^2 * var(ens[n,])). Negative variances are set to zero. Note that parameters = list(r1=0, r2=0, a=1, s1=0, s2=1) yields the same dressed ensemble as dressing.method="silverman".

"akd.fit": Affine Kernel Dressing with fitted parameters. The required parameters is list(obs), where `obs` is a vector of observations which are used to optimize the parameters r1, r2, a, s1, s2 by CRPS minimization. See ?FitAkdParameters for more information.

References

Silverman, B.W. (1998). Density Estimation for Statistics and Data Analysis. London: Chapman & Hall/CRC. ISBN 0-412-24620-1.

Broecker J. and Smith L. (2008). From ensemble forecasts to predictive distribution functions. Tellus (2008), 60A, 663--678. DOI 10.1111/j.1600-0870.2008.00333.x.

Examples

  # Example:
  ens <- matrix(rnorm(500),100,5)
  obs <- rnorm(100)
  d.silverman <- DressEnsemble(ens)
  d.akd <- DressEnsemble(ens, dressing.method="akd", 
                         parameters=list(r1=0, r2=0, a=1, 
                                         s1=0, s2=0))
  d.akd.fit <- DressEnsemble(ens, dressing.method="akd.fit", 
                             parameters=list(obs=obs))